Question

Let x = boiler steam pressure in 100 lb/ in2 and let y = critical sheer strength of boiler plate steel joints in tons/ in2. We have the following data for a series of factory boilers. x 4 5 6 8 10 y 3.4 4.2 6.3 10.9 13.3 (a) Make the logarithmic transformations x' = log (x) and y' = log (y). Then make a scatter plot of the (x', y') values. Does a linear equation seem to be a good fit to this plot? The transformed data fit a straight line well. The transformed data does not fit a straight line well. The data seem to have a parabolic shape. The transformed data does not fit a straight line well. The data seem to explode as x increases. The transformed data does not fit a straight line well. The data seem to explode as x decreases. Correct: Your answer is correct. (b) Use the (x', y') data points and a calculator with regression keys to find the least-squares equation y' = a + bx'. What is the correlation coefficient? (Use 3 decimal places.) y' = + x' r = (c) Use the results of part (b) to find estimates for α and β in the power law y = αxβ. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. (Use 3 decimal places.) α = β = y hat = · x^

Please show and explain how you get your answer in each step and do it in print if possible.

Thank.

Answer 1

(a) The transformed data fit a straight line well.

The option (A) is correct. (The transformed data fit a straight line well). the values are not exploding. Other option are incorrect.

The following scatter plot is obtained based on the logarithmic transformed data:

B) Using Excel we have found equation of regression line:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990672
R Square	0.981431
Adjusted R Square	0.975241
Standard Error	0.040266
Observations	5

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.45119	0.102786	-4.38959	0.021902	-0.7783	-0.12408	-0.7783	-0.12408
log(X)	1.599913	0.127058	12.59195	0.00108	1.195556	2.004269	1.195556	2.004269

herefore, we find that the regression equation is:

log(Y) = -0.451 + 1.600*log(X)

i.e. Y'=-0.451 + 1.600 *X'

from above table we can find correlation coefficient.

Multiple R. This is the correlation coefficient. It tells you how strong the linear relationship

Hence correlation coefficient is 0.991.

(c) Use the results of part (b) to find estimates for ? and ? in the power law y = ?x^?. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. (Use 3 decimal places.)

function value

mean of x= 0.783

mean of y =0.790

correlation coefficient r= 0.991

? =1.161

? =1.580

?=1.161*x^1.580